MATH 112 PRACTICE TEST 1 FALL 2007
Solve the linear inequality. Use INTERVAL NOTATION
to express the solution set, and graph the solution set on a
number line. Show your work.
x - 2 x - 4
1
1)
≥ + 15
20
60
-6 -5 -4 -3 -2 -1 0
1
2
3
4
5
Solve the absolute value inequality. Use INTERVAL
NOTATION to express the solution set and graph the
solution set on a number line. Show your work.
4) |x + 3| > 2
6
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
Determine whether the relation is a function.
5) {(-4, 6), (-1, 3), (3, 3), (8, -9)}
Solve the compound inequality. Use INTERVAL
NOTATION to express the solution set and graph the
solution set on a number line.
2) 3 ≤ 2x - 5 ≤ 9
6) {(-6, 8), (-3, 8), (2, -7), (2, -9)}
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Give the domain and range of the relation.
7) {(-1, -4), (-2, -3), (-2, 0), (7, 3), (23, 5)}
Solve the absolute value inequality. Use INTERVAL
NOTATION to express the solution set and graph the
solution set on a number line. Show your work.
3) |x - 4| < 6
8) {(-8, -3), (3, 5), (9, 8), (-6, 2), (-4, 7)}
-2
0
2
4
6
8
10
12
14
16
18
6
7
Determine whether the equation defines y as a function
of x.
9) x + y2 = 1
16) f(x) = x2 + 5
;
x3 - 3x
f(-5)
10) y = x2
Use the vertical line test to determine whether or not the
graph is a graph in which y is a function of x.
17)
11) x + y3 = 1
y
Evaluate the function at the given value of the
independent variable and simplify.
12) f(x) = 5x2 + 2x + 3; f(x - 1)
x
18)
13) f(x) = x + 13;
f(-4)
14) h(x) = x - 13 ;
h(19)
15) g(x) = 4x + 2;
g(x + 1)
y
x
21) A graph of a function f is shown below. Find
f(0).
Use the graph to find the indicated function value.
19) y = f(x). Find f(-4)
5
y
y
3
4
3
2
(0, 2)
2
1
1
(1, 0)
-5
-4
-3
-2
-1
1
2
3
4
5 x
-3
-1
-2
-1
1
2
3
-1
-2
-3
-2
(2, -2)
-4
-3
-5
Evaluate as requested.
20) A graph of a function g is shown below. Find
g(-1.5).
Use the graph to determine the functionʹs domain and
range.
22)
6
y
5
(-1.5, 3.9375)
4
y
5
4
(1.5, 3.9375)
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
-1
-5
-4
-3
-2
x
-1
1
2
3
4
5
-1
-2
-3
(-2.2, -4.0656)
-4
-5
(2.1, -1.8081)
x
-2
-3
-4
-5
-6
1
2
3
4
5
6 x
23)
6
26) f(x) = y
1
5x
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-2
-3
-4
-5
For each function f, construct and simplify the difference
f(x + h) - f(x)
.
quotient h
-6
27) f(x) = 8x2 + 3x
24)
6
y
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
-2
-3
-4
-5
-6
5
6 x
Evaluate the piecewise function at the given value of the
independent variable.
28)
-5x + 1 if x < -2
f(x) =
2x + 3 if x ≥ -2
Determine f(-3).
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
25) f(x) = x2 + 9x - 8
29)
-4x + 3 if x < -2
f(x) =
-2x + 1 if x ≥ -2
Determine f(-2).
30)
33)
x - 3 if x > -2
f(x) =
f(x) =
-(x - 3) if x ≤ -2
x2 - 9
, for x ≠ -3
x + 3
4, for x = -3
Determine f(-3).
y
8
6
4
Graph the function.
31)
-5, for x ≥ 1
f(x) =
-2 - x, for x < 1
6
2
-6
-4
-2
2
4
6
x
-2
y
-4
4
-6
2
-8
-10
-6
-4
-2
2
4
6 x
-2
34)
-4
f(x) =
-6
x2 - 1
, for x ≠ -1
x - 1
- 2, for x = 1
32)
5
x - 3, for x > 0
4
f(x) =
3
-1, for x ≤ 0
6
2
y
1
4
-6 -5 -4 -3 -2 -1
-1
2
-2
-3
-6
-4
-2
2
-2
-4
-6
y
4
6 x
-4
-5
1
2
3
4
5
6 x
Use the graph to determine the functionʹs domain and
range.
35)
10
38) Decreasing
y
8
y
8
4
6
4
-12
2
-10 -8
-6
-4
-2
2
4
6
8
-6
6
12
x
4
5 x
-4
x
-2
-4
-8
-6
-8
-10
39) Constant
5
y
4
3
Identify the intervals where the function is changing as
requested.
36) Constant
5
2
1
y
-5
-4
-3
-2
-1
1
4
-1
3
-2
2
-3
1
-4
-5
-4
-3
-2
-1
1
2
3
4
x
-1
-2
-3
-4
-5
37) Increasing
5
y
4
3
2
1
-10-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5 6 7 8 9
x
2
3
The graph of a function f is given. Use the graph to
answer the question.
40) Find the numbers, if any, at which f has a
relative minimum. What are the relative
minima?
5
Determine algebraically whether the function is even,
odd, or neither even nor odd.
42) f(x) = -6x4 + 3x - 9
y
4
3
43) f(x) = 13x - 8 x
2
1
-5
-4
-3
-2
-1
1
2
3
5 x
4
-1
-2
-3
44) f(x) = 7x4 + 2x - 7
-4
-5
A) f has a relative minimum at x = -2; the
relative minimum is 0
B) f has a relative minimum at x = -2 and 2;
the relative minimum is 0
C) f has a relative minimum at x = 0; the
relative minimum is 1
D) f has no relative minimum
Use the graph of the given function to find any relative
maxima and relative minima.
41) f(x) = x3 - 12x + 2
22
20
18
16
14
12
10
8
6
4
2
-6
-5
-4
-3
-2
-1 -2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
y
45) f(x) = -2x5 + 8x3
Use possible symmetry to determine whether the graph is
the graph of an even function, an odd function, or a
function that is neither even nor odd.
46)
y
10
8
6
4
2
1
2
3
4
5
A) maximum: (-2, 18) and (0, 0); minimum:
(2, -14)
B) maximum: (2, -14); minimum: (-2, 18)
C) minimum: (2, -14); maximum: (-2, 18)
D) no maximum or minimum
6
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
2
4
6
8 10 x
47)
If f(x) = int (x), find the function value.
50) f(98)
y
10
8
6
51) f(-28.63)
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
52) f(21.9738)
-6
-8
-10
Determine if the given function is even, odd, or neither
even nor odd.
48)
5
53) f( )
2
y
10
Use the shape of the graph to name the function.
54)
5
y
-10
-5
5
10 x
-5
x
-10
A) Square root function
B) Absolute value function
C) Identity function
D) Constant function
49)
y
10
55)
5
y
-10
-5
5
10 x
-5
x
-10
A) Constant function
B) Standard cubic function
C) Standard quadratic function
D) Square root function
56)
Begin by graphing the standard square root function f(x)
= x . Then use transformations of this graph to graph the
given function.
59) g(x) = x - 1
y
10
8
6
x
y
4
2
A) Standard quadratic function
B) Square root function
C) Constant function
D) Standard cubic function
-10 -8 -6 -4 -2
-2
-4
-6
2 4
6 8 10 x
-8
-10
57)
y
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
given function.
60) g(x) = x2 - 2
x
10
A) Constant function
B) Standard quadratic function
C) Standard cubic function
D) Square root function
y
8
6
4
2
-10 -8 -6 -4 -2-2
2 4
6 8 10 x
-4
-6
-8
-10
58)
y
x
A) Absolute value function
B) Standard cubic function
C) Identity function
D) Constant function
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function.
61) g(x) = x + 3
10
8
6
y
4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
2 4
6 8 10 x
Begin by graphing the standard quadratic function f(x) =
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
given function.
62) h(x) = (x + 2)2
x 2 . Then use transformations of this graph to graph the
given function.
65) h(x) = -(x + 2)2
10
y
8
6
10
8
6
4
2
4
2
-10 -8 -6 -4 -2
-2
-4
-6
2 4 6
8 10 x
Begin by graphing the standard square root function f(x)
= x . Then use transformations of this graph to graph the
given function.
63) h(x) = x + 2
y
-10 -8 -6 -4 -2-2
2 4 6
8 10 x
-4
-6
-8
y
-10 -8 -6 -4 -2
-2
-4
2 4
6 8 10 x
-6
-8
-10
-10
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function.
64) h(x) = x + 2 + 2
y
8
6
4
2
-8
-10
6 8 10 x
6
4
2
2
-10 -8 -6 -4 -2
-2
-4
-6
2 4
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function.
66) h(x) = - x + 2
10
8
6
4
10
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
-8
-10
10
8
y
2 4 6
8 10 x
Use the graph of the function f, plotted with a solid line,
to sketch the graph of the given function g.
67) g(x) = - f(x) + 2
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
y = f(x)
1 2 3 4 5 6 x
Begin by graphing the standard absolute value function
f(x) = x . Then use transformations of this graph to graph
the given function.
68) h(x) = 2 x - 2
10
8
6
Begin by graphing the standard square root function f(x)
= x . Then use transformations of this graph to graph the
given function.
71) g(x) = - x + 2 - 2
y
10
y
8
6
4
4
2
2
-10 -8 -6 -4 -2-2
2 4
6 8 10 x
-10 -8 -6 -4 -2-2
-4
-6
-8
-4
-6
-8
-10
-10
Use the graph of y = f(x) to graph the given function g.
69) g(x) = 2f(x)
2 4
6 8 10 x
Use the graph of the function f, plotted with a solid line,
to sketch the graph of the given function g.
72) g(x) = -f(x - 1) + 2
y
12
10
6
5
4
3
2
1
8
6
4
2
-12 -10 -8 -6 -4 -2
-2
-4
2 4
6 8 10 12 x
-6
-8
-10
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
y = f(x)
1 2 3 4 5 6 x
-12
Begin by graphing the standard quadratic function f(x) =
x 2 . Then use transformations of this graph to graph the
Find the domain of the function.
x2
73) f(x) = x2 + 4
given function.
70) h(x) = -(x + 4)2 + 5
10
8
6
y
74) g(x) = 4
2
-10 -8 -6 -4 -2-2
-4
-6
-8
-10
2 4
6 8 10 x
x
x2 - 16
75) h(x) = 76)
x - 3
Given functions f and g, determine the domain of f + g.
4x
5
80) f(x) = ,
g(x) = x - 4
x + 1
x3 - 81x
For the given functions f and g , find the indicated
composition.
81) f(x) = 9x2 - 3x, g(x) = 12x - 8
x
x - 6
77) f(x) = (f∘g)(2)
1
4
+ x - 4 x + 6
Given functions f and g, perform the indicated
operations.
78) f(x) = 7x - 3,
g(x) = 9x - 2
Find f - g.
82) f(x) = 4x 2 + 6x + 4,
(g∘f)(x)
83) f(x) = 3x + 10,
(f∘g)(x)
g(x) = 6x - 5
g(x) = 3x - 1
Find the domain of the composite function f∘g.
5
,
g(x) = x + 5
84) f(x) = x + 7
79) f(x) = 7x - 3,
Find fg.
g(x) = 5x + 9
85) f(x) = 5
,
x + 8
g(x) = 16
x
86) f(x) = x; g(x) = 2x + 4
Answer Key
Testname: MATH 112 PRACTICE TEST 1 FA 07
1) [-3, ∞)
31)
6
-20 -16 -12 -8 -4 0
4
y
8 12 16 20 24 28
4
2) [4, 7]
2
-1
0
1
2
3
4
5
6
7
8
9
10 11 12
-6
3) (-2, 10)
-2
-4
-2
2
4
6 x
2
4
6 x
-2
0
2
4
6
8
10
12
14
16
18
-4
20
-6
4)
32)
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
6
5) Function
6) Not a function
7) domain: {-1, 7, -2, 23}; range: {-4, -3, 0, 3, 5}
8) domain = {-8, 9, -6, -4, 3}; range = {-3, 8, 2, 7, 5}
9) y is not a function of x
10) y is a function of x
11) y is a function of x
12) 5x2 - 8x + 6
13) 3
14) 6
4
2
-6
-4
-2
-2
-4
-6
33)
15) 4x + 6
3
16) - 11
17) not a function
18) function
19) 4
20) 3.9375
21) 2
22) domain: (-∞, ∞)
range: [-4, ∞)
23) domain: (-∞, ∞)
range: (-∞, 3]
24) domain: [0, ∞)
range: [-2, ∞)
25) 2x + h + 9
-1
26) 5x (x + h)
27) 16x + 8h + 3
28) 16
29) 5
30) 6
y
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
34)
y
10
5
-10
-5
-5
-10
35) domain: (-∞, ∞)
range: [0, 6]
36) (-∞, -1) or (3, ∞)
37) (3, ∞)
Answer Key
Testname: MATH 112 PRACTICE TEST 1 FA 07
38) (5, 12)
39) (-1, 1)
40) B
41) C
42) Neither
43) Neither
44) Neither
45) Odd
46) Even
47) Neither
48) Odd
49) Even
50) 98
51) -29
52) 21
53) 2
54) C
55) C
56) D
57) D
58) A
59)
61)
10
8
y
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
2 4
6 8 10 x
2 4
6 8 10 x
2 4
6 8 10 x
2 4
6 8 10 x
-8
-10
62)
10
8
y
6
4
2
-10 -8 -6 -4 -2
-2
-4
10
8
6
-6
-8
-10
y
63)
4
2
-10 -8 -6 -4 -2
-2
-4
2 4 6
10
8
6
8 10 x
4
2
-6
-8
-10
-10 -8 -6 -4 -2
-2
-4
-6
60)
10
8
6
-8
-10
y
64)
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
y
2 4 6
8 10 x
10
8
6
y
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
Answer Key
Testname: MATH 112 PRACTICE TEST 1 FA 07
65)
69)
10
8
6
y
14
12
10
8
6
4
4
2
-10 -8 -6 -4 -2
-2
-4
-6
2 4 6
8 10 x
2
-8
-10
-12 -10 -8 -6 -4 -2
-2
-4
-6
10
-8
-10
-12
66)
y
10
8
-10 -8 -6 -4 -2
-2
-4
-6
2 4 6
-10 -8 -6 -4 -2-2
-4
67)
6 8 10 x
2 4
6 8 10 x
71)
10
8
y
6
4
2
1 2 3 4 5 6 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
y
8
6
4
72)
6
5
4
3
2
1
2
2 4 6
8 10 x
-4
-6
-8
-10
2 4
-6
-8
-10
y
68)
-10 -8 -6 -4 -2-2
y
6
4
2
8 10 x
-8
-10
10
6 8 10 12 x
70)
4
2
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
2 4
-14
8
6
6
5
4
3
2
1
y
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
73) (-∞, ∞)
y
1 2 3 4 5 6 x
Answer Key
Testname: MATH 112 PRACTICE TEST 1 FA 07
74) (-∞, -4) ∪ (-4, 4) ∪ (4, ∞)
75) (-∞, -9) ∪ (-9, 0) ∪ (0, 9) ∪ (9, ∞)
76) (6, ∞)
77) (-∞, -6) ∪ (-6, 4) ∪ (4, ∞)
78) -2x - 1
79) 35x2 + 48x - 27
80) (-∞, -1) ∪ (-1, 4) ∪ (4, ∞)
81) 2256
82) 24x2 + 36x + 19
83) 9x + 7
84) (-∞, -12) ∪ (-12, ∞)
85) (-∞, -2) ∪ (-2, 0) ∪ (0, ∞)
86) [-2, ∞)